The Republican-led state Senate won’t extend mayoral control of New York City schools as part of its state budget plan unveiled Wednesday — creating a potential headache for Mayor de Blasio.

The law giving the mayor authority to run the public schools expires on June 30.

In his executive budget, Gov. Cuomo recommended that mayoral control be renewed for three years. The Democratic-run ­Assembly called for an even longer extension, to 2022.

But nothing can happen without the Senate.

Albany insiders said Senate Republicans want to slow down approval in order to teach a lesson to de Blasio, who campaigned last year for Dems trying to regain control of the legislative body.

“That’s a ridiculous assertion. It’s about educating kids in the city of New York,” insisted senate Education Committee Chairman John Flanagan (R-Suffolk).

Flanagan said the issue of mayoral control should be dealt with separately from the budget. City Hall has so far been unresponsive to requests to testify at a public hearing or meet on the issue, Flanagan said.